Here's my wrapping up Mayhem 1-10 (except Mayhem 2 which I think I'll leave to ClamSpammer
):
Confirmed Mayhem 7. non-100% (can't dig or build fast enough for 2nd lemming, and even if somehow there's a way, you'll probably run out of skills to finish the actual level). My solution loses 2. I could attach a replay but this is one that is more fun to figure out on your own, it is quite conventional and should be doable by many here.
Mayhem 5 is obviously not possible because there are no known solution that doesn't use blockers. Mayhem 9 is also pretty obviously impossible.
This leaves Mayhem 6, which unfortunately has eluded me so far. I've tried a number of things only to either be short 1 or 2 builders, or run out of time (as in not even close). I haven't given up yet though, and maybe others will have better luck with this one.
[edit: whoops, forgot Mayhem 4. It was obviously very annoying to do, but I did get a solution that truly uses only 1 lemming (see text version of replay for proof, attached). It saves 82% while the requirement is 80%. Whether 100% is possible remains to be seen.]